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19  Machine Learning

19.1 Getting Started

19.1.1 Load Packages

library("petersenlab")
library("parallel")
library("doParallel")
library("missRanger")
library("powerjoin")
library("caret")
library("gpboost")
library("tidyverse")

19.1.2 Load Data

# Downloaded Data - Processed
load(file = "./data/nfl_players.RData")
load(file = "./data/nfl_teams.RData")
load(file = "./data/nfl_rosters.RData")
load(file = "./data/nfl_rosters_weekly.RData")
load(file = "./data/nfl_schedules.RData")
load(file = "./data/nfl_combine.RData")
load(file = "./data/nfl_draftPicks.RData")
load(file = "./data/nfl_depthCharts.RData")
load(file = "./data/nfl_pbp.RData")
load(file = "./data/nfl_4thdown.RData")
load(file = "./data/nfl_participation.RData")
#load(file = "./data/nfl_actualFantasyPoints_weekly.RData")
load(file = "./data/nfl_injuries.RData")
load(file = "./data/nfl_snapCounts.RData")
load(file = "./data/nfl_espnQBR_seasonal.RData")
load(file = "./data/nfl_espnQBR_weekly.RData")
load(file = "./data/nfl_nextGenStats_weekly.RData")
load(file = "./data/nfl_advancedStatsPFR_seasonal.RData")
load(file = "./data/nfl_advancedStatsPFR_weekly.RData")
load(file = "./data/nfl_playerContracts.RData")
load(file = "./data/nfl_ftnCharting.RData")
load(file = "./data/nfl_playerIDs.RData")
load(file = "./data/nfl_rankings_draft.RData")
load(file = "./data/nfl_rankings_weekly.RData")
load(file = "./data/nfl_expectedFantasyPoints_weekly.RData")
load(file = "./data/nfl_expectedFantasyPoints_pbp.RData")

# Calculated Data - Processed
load(file = "./data/nfl_actualStats_career.RData")
load(file = "./data/nfl_actualStats_seasonal.RData")
load(file = "./data/player_stats_weekly.RData")
load(file = "./data/player_stats_seasonal.RData")

19.1.3 Specify Options

options(scipen = 999) # prevent scientific notation

19.2 Overview of Machine Learning

Machine learning takes us away from focusing on causal inference. Machine learning does not care about which processes are causal—i.e., which processes influence the outcome. Instead, machine learning cares about prediction—it cares about a predictor variable to the extent that it increases predictive accuracy regardless of whether it is causally related to the outcome.

Machine learning can be useful for leveraging big data and lots of predictor variable to develop predictive models with greater accuracy. However, many machine learning techniques are black boxes—it is often unclear how or why certain predictions are made, which can make it difficult to interpret the model’s decisions and understand the underlying relationships between variables. Machine learning tends to be a data-driven, atheoretical technique. This can result in overfitting. Thus, when estimating machine learning models, it is common to keep a hold-out sample for use in cross-validation to evaluate the extent of shrinkage of model coefficients. The data that the model is trained on is known as the “training data”. The data that the model was not trained on but is then is independently tested on—i.e., the hold-out sample—is the “test data”. Shrinkage occurs when predictor variables explain some random error variance in the original model. When the model is applied to an independent sample (i.e., the test data), the predictive model will likely not perform quite as well, and the regressions coefficients will tend to get smaller (i.e., shrink).

If the test data were collected as part of the same processes as the original data and were merely held out for purposes of analysis, this is called internal cross-validation. If the test data were collected separately from the original data used to train the model, this is called external cross-validation.

Most machine learning methods were developed with cross-sectional data in mind. That is, they assume that each person has only one observation on the outcome variable. However, with longitudinal data, each person has multiple observations on the outcome variable.

When performing machine learning, various approaches may help address this:

• transform data from long to wide form, so that each person has only one row
• when designing the training and test sets, keep all measurements from the same person in the same data object (either the training or test set); do not have some measurements from a given person in the training set and other measurements from the same person in the test set
• use a machine learning approach that accounts for the clustered/nested nature of the data

19.3 Types of Machine Learning

There are many approaches to machine learning. This chapter discusses several key ones:

• supervised learning
  • continuous outcome (i.e., regression)
    • linear regression
    • lasso regression
    • ridge regression
    • elastic net regression
  • categorical outcome (i.e., classification)
    • logistic regression
    • support vector machine
    • random forest
    • extreme gradient boosting
• unsupervised learning
  • clustering
  • principal component analysis
• semi-supervised learning
• reinforcement learning
  • deep learning
• ensemble

Ensemble machine learning methods combine multiple machine learning approaches with the goal that combining multiple approaches might lead to more accurate predictions that any one method might be able to achieve on its own.

19.3.1 Supervised Learning

[DEFINE SUPERVISED LEARNING]

Unlike linear and logistic regression, various machine learning techniques can handle multicollinearity, including LASSO regression, ridge regression, and elastic net regression. Least absolute shrinkage and selection operator (LASSO) regression helps perform selection of which predictor variables to keep in the model by shrinking some coefficients to zero. Ridge regression shrinks the coefficients of predictor variables toward zero, but not to zero, so it does not perform selection of which predictor variables to retain; this allows it to allow nonzero coefficients for multiple correlated predictor variables in the context of multicollinearity. Elastic net involves a combination of LASSO and ridge regression; it performs selection of which predictor variables to keep by shrinking the coefficients of some predictor variables to zero, and it shrinks the coefficients of some predictor variables toward zero, to address multicollinearity.

Unless interactions or nonlinear terms are specified, linear, logistic, LASSO, ridge, and elastic net regresstion do not account for interactions among the predictor variables or for nonlinear associations between the predictor variables and the outcome variable. By contrast, random forests and extreme gradient boosting do account for interactions among the predictor variables and for nonlinear associations between the predictor variables and the outcome variable.

19.3.2 Unsupervised Learning

[DEFINE UNSUPERVISED LEARNING]

We describe cluster analysis in Chapter 21. We describe principal component analysis in Chapter 23.

19.3.3 Semi-supervised Learning

[DEFINE SEMI-SUPERVISED LEARNING]

19.3.4 Reinforcement Learning

[DEFINE REINFORCEMENT LEARNING]

19.4 Data Processing

19.4.1 Prepare Data for Merging

# Prepare data for merging
#-todo: calculate years_of_experience
## Use common name for the same (gsis_id) ID variable

#nfl_actualFantasyPoints_player_weekly <- nfl_actualFantasyPoints_player_weekly %>% 
#  rename(gsis_id = player_id)
#
#nfl_actualFantasyPoints_player_seasonal <- nfl_actualFantasyPoints_player_seasonal %>% 
#  rename(gsis_id = player_id)

player_stats_seasonal_offense <- player_stats_seasonal %>% 
  filter(position_group %in% c("QB","RB","WR","TE")) %>% 
  rename(gsis_id = player_id)

player_stats_weekly_offense <- player_stats_weekly %>% 
  filter(position_group %in% c("QB","RB","WR","TE")) %>% 
  rename(gsis_id = player_id)

nfl_expectedFantasyPoints_weekly <- nfl_expectedFantasyPoints_weekly %>% 
  rename(gsis_id = player_id)

## Rename other variables to ensure common names

## Ensure variables with the same name have the same type
nfl_players <- nfl_players %>% 
  mutate(
    birth_date = as.Date(birth_date),
    jersey_number = as.character(jersey_number),
    gsis_it_id = as.character(gsis_it_id),
    years_of_experience = as.integer(years_of_experience))

player_stats_seasonal_offense <- player_stats_seasonal_offense %>% 
  mutate(
    birth_date = as.Date(birth_date),
    jersey_number = as.character(jersey_number),
    gsis_it_id = as.character(gsis_it_id))

nfl_rosters <- nfl_rosters %>% 
  mutate(
    draft_number = as.integer(draft_number))

nfl_rosters_weekly <- nfl_rosters_weekly %>% 
  mutate(
    draft_number = as.integer(draft_number))

nfl_depthCharts <- nfl_depthCharts %>% 
  mutate(
    season = as.integer(season))

nfl_expectedFantasyPoints_weekly <- nfl_expectedFantasyPoints_weekly %>% 
  mutate(
    season = as.integer(season),
    receptions = as.integer(receptions)) %>% 
  distinct(gsis_id, season, week, .keep_all = TRUE) # drop duplicated rows

## Rename variables
nfl_draftPicks <- nfl_draftPicks %>%
  rename(
    games_career = games,
    pass_completions_career = pass_completions,
    pass_attempts_career = pass_attempts,
    pass_yards_career = pass_yards,
    pass_tds_career = pass_tds,
    pass_ints_career = pass_ints,
    rush_atts_career = rush_atts,
    rush_yards_career = rush_yards,
    rush_tds_career = rush_tds,
    receptions_career = receptions,
    rec_yards_career = rec_yards,
    rec_tds_career = rec_tds,
    def_solo_tackles_career = def_solo_tackles,
    def_ints_career = def_ints,
    def_sacks_career = def_sacks
  )

## Subset variables
nfl_expectedFantasyPoints_weekly <- nfl_expectedFantasyPoints_weekly %>% 
  select(gsis_id:position, contains("_exp"), contains("_diff"), contains("_team")) #drop "raw stats" variables (e.g., rec_yards_gained) so they don't get coalesced with actual stats

# Check duplicate ids
player_stats_seasonal_offense %>% 
  group_by(gsis_id, season) %>% 
  filter(n() > 1) %>% 
  head()

nfl_advancedStatsPFR_seasonal %>% 
  group_by(gsis_id, season) %>% 
  filter(n() > 1, !is.na(gsis_id)) %>% 
  select(gsis_id, pfr_id, season, team, everything()) %>% 
  head()

Identify objects with shared variable names:

dplyr::intersect(
  names(nfl_players),
  names(nfl_draftPicks))

[1] "gsis_id"  "position"

length(na.omit(nfl_players$position)) # use by default (more cases)

[1] 21360

length(na.omit(nfl_draftPicks$position))

[1] 2855

dplyr::intersect(
  names(player_stats_seasonal_offense),
  names(nfl_advancedStatsPFR_seasonal))

[1] "gsis_id" "season"  "team"    "age"    

length(na.omit(player_stats_seasonal_offense$season)) # use by default (more cases)

[1] 14859

length(na.omit(nfl_advancedStatsPFR_seasonal$season))

[1] 10395

length(na.omit(player_stats_seasonal_offense$team)) # use by default (more cases)

[1] 14858

length(na.omit(nfl_advancedStatsPFR_seasonal$team))

[1] 10395

length(na.omit(player_stats_seasonal_offense$age)) # use by default (more cases)

[1] 14859

length(na.omit(nfl_advancedStatsPFR_seasonal$age))

[1] 10325

dplyr::intersect(
  names(nfl_rosters_weekly),
  names(nfl_expectedFantasyPoints_weekly))

[1] "gsis_id"   "season"    "week"      "position"  "full_name"

length(na.omit(nfl_rosters_weekly$season)) # use by default (more cases)

[1] 845134

length(na.omit(nfl_expectedFantasyPoints_weekly$season))

[1] 100272

length(na.omit(nfl_rosters_weekly$week)) # use by default (more cases)

[1] 841942

length(na.omit(nfl_expectedFantasyPoints_weekly$week))

[1] 100272

length(na.omit(nfl_rosters_weekly$position)) # use by default (more cases)

[1] 845101

length(na.omit(nfl_expectedFantasyPoints_weekly$position))

[1] 97815

length(na.omit(nfl_rosters_weekly$full_name)) # use by default (more cases)

[1] 845118

length(na.omit(nfl_expectedFantasyPoints_weekly$full_name))

[1] 97815

19.4.2 Merge Data

To merge data, we use the powerjoin package (Fabri, 2022):

# Create lists of objects to merge, depending on data structure: id; or id-season; or id-season-week
#-todo: remove redundant variables
playerListToMerge <- list(
  nfl_players %>% filter(!is.na(gsis_id)),
  nfl_draftPicks %>% filter(!is.na(gsis_id)) %>% select(-season)
)

playerSeasonListToMerge <- list(
  player_stats_seasonal_offense %>% filter(!is.na(gsis_id), !is.na(season)),
  nfl_advancedStatsPFR_seasonal %>% filter(!is.na(gsis_id), !is.na(season))
)

playerSeasonWeekListToMerge <- list(
  nfl_rosters_weekly %>% filter(!is.na(gsis_id), !is.na(season), !is.na(week)),
  #nfl_actualStats_offense_weekly,
  nfl_expectedFantasyPoints_weekly %>% filter(!is.na(gsis_id), !is.na(season), !is.na(week))
  #nfl_advancedStatsPFR_weekly,
)

playerSeasonWeekPositionListToMerge <- list(
  nfl_depthCharts %>% filter(!is.na(gsis_id), !is.na(season), !is.na(week))
)

# Merge data
playerMerged <- playerListToMerge %>% 
  reduce(
    powerjoin::power_full_join,
    by = c("gsis_id"),
    conflict = coalesce_xy) # where the objects have the same variable name (e.g., position), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2

playerSeasonMerged <- playerSeasonListToMerge %>% 
  reduce(
    powerjoin::power_full_join,
    by = c("gsis_id","season"),
    conflict = coalesce_xy) # where the objects have the same variable name (e.g., team), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2

playerSeasonWeekMerged <- playerSeasonWeekListToMerge %>% 
  reduce(
    powerjoin::power_full_join,
    by = c("gsis_id","season","week"),
    conflict = coalesce_xy) # where the objects have the same variable name (e.g., position), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2

Identify objects with shared variable names:

dplyr::intersect(
  names(playerSeasonMerged),
  names(playerMerged))

 [1] "gsis_id"                  "position"                
 [3] "position_group"           "first_name"              
 [5] "last_name"                "esb_id"                  
 [7] "display_name"             "rookie_year"             
 [9] "college_conference"       "current_team_id"         
[11] "draft_club"               "draft_number"            
[13] "draftround"               "entry_year"              
[15] "football_name"            "gsis_it_id"              
[17] "headshot"                 "jersey_number"           
[19] "short_name"               "smart_id"                
[21] "status"                   "status_description_abbr" 
[23] "status_short_description" "uniform_number"          
[25] "height"                   "weight"                  
[27] "college_name"             "birth_date"              
[29] "suffix"                   "years_of_experience"     
[31] "pfr_player_name"          "team"                    
[33] "age"                     

seasonalData <- powerjoin::power_full_join(
  playerSeasonMerged,
  playerMerged %>% select(-age, -years_of_experience, -team, -team_abbr, -team_seq, -current_team_id), # drop variables from id objects that change from year to year (and thus are not necessarily accurate for a given season)
  by = "gsis_id",
  conflict = coalesce_xy # where the objects have the same variable name (e.g., position), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2
) %>% 
  filter(!is.na(season)) %>% 
  select(gsis_id, season, player_display_name, position, team, games, everything())

dplyr::intersect(
  names(playerSeasonWeekMerged),
  names(seasonalData))

 [1] "gsis_id"                 "season"                 
 [3] "week"                    "team"                   
 [5] "jersey_number"           "status"                 
 [7] "first_name"              "last_name"              
 [9] "birth_date"              "height"                 
[11] "weight"                  "college"                
[13] "pfr_id"                  "headshot_url"           
[15] "status_description_abbr" "football_name"          
[17] "esb_id"                  "gsis_it_id"             
[19] "smart_id"                "entry_year"             
[21] "rookie_year"             "draft_club"             
[23] "draft_number"            "position"               

seasonalAndWeeklyData <- powerjoin::power_full_join(
  playerSeasonWeekMerged,
  seasonalData,
  by = c("gsis_id","season"),
  conflict = coalesce_xy # where the objects have the same variable name (e.g., position), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2
) %>% 
  filter(!is.na(week)) %>% 
  select(gsis_id, season, week, full_name, position, team, everything())

# Duplicate cases
seasonalData %>% 
  group_by(gsis_id, season) %>% 
  filter(n() > 1) %>% 
  head()

seasonalAndWeeklyData %>% 
  group_by(gsis_id, season, week) %>% 
  filter(n() > 1) %>% 
  head()

19.4.3 Additional Processing

# Convert character and logical variables to factors
seasonalData <- seasonalData %>% 
  mutate(
    across(
      where(is.character),
      as.factor
    ),
    across(
      where(is.logical),
      as.factor
    )
  )

19.4.4 Fill in Missing Data for Static Variables

seasonalData <- seasonalData %>% 
  arrange(gsis_id, season) %>% 
  group_by(gsis_id) %>% 
  fill(
    player_name, player_display_name, pos, position, position_group,
    .direction = "downup") %>% 
  ungroup()

19.4.5 Lag Fantasy Points

seasonalData_lag <- seasonalData %>% 
  arrange(gsis_id, season) %>% 
  group_by(gsis_id) %>% 
  mutate(
    fantasyPoints_lag = lead(fantasyPoints)
  ) %>% 
  ungroup()

seasonalData_lag %>% 
  select(gsis_id, player_display_name, season, fantasyPoints, fantasyPoints_lag) # verify that lagging worked as expected

19.4.6 Subset to Predictor Variables and Outcome Variable

seasonalData_lag %>% select_if(~class(.) == "Date")

seasonalData_lag %>% select_if(is.character)

seasonalData_lag %>% select_if(is.factor)

seasonalData_lag %>% select_if(is.logical)

dropVars <- c(
  "birth_date", "loaded", "full_name", "player_name", "player_display_name", "display_name", "suffix", "headshot_url", "player", "pos",
  "espn_id", "sportradar_id", "yahoo_id", "rotowire_id", "pff_id", "fantasy_data_id", "sleeper_id", "pfr_id",
  "pfr_player_id", "cfb_player_id", "pfr_player_name", "esb_id", "gsis_it_id", "smart_id",
  "college", "college_name", "team_abbr", "current_team_id", "college_conference", "draft_club", "status_description_abbr",
  "status_short_description", "short_name", "headshot", "uniform_number", "jersey_number", "first_name", "last_name",
  "football_name", "team")

seasonalData_lag_subset <- seasonalData_lag %>% 
  dplyr::select(-any_of(dropVars))

19.4.7 Separate by Position

seasonalData_lag_subsetQB <- seasonalData_lag_subset %>% 
  filter(position == "QB") %>% 
  select(
    gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic,
    height, weight, rookie_year, draft_number,
    fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag,
    completions:rushing_2pt_conversions, special_teams_tds, contains(".pass"), contains(".rush"))

seasonalData_lag_subsetRB <- seasonalData_lag_subset %>% 
  filter(position == "RB") %>% 
  select(
    gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic,
    height, weight, rookie_year, draft_number,
    fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag,
    carries:special_teams_tds, contains(".rush"), contains(".rec"))

seasonalData_lag_subsetWR <- seasonalData_lag_subset %>% 
  filter(position == "WR") %>% 
  select(
    gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic,
    height, weight, rookie_year, draft_number,
    fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag,
    carries:special_teams_tds, contains(".rush"), contains(".rec"))

seasonalData_lag_subsetTE <- seasonalData_lag_subset %>% 
  filter(position == "TE") %>% 
  select(
    gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic,
    height, weight, rookie_year, draft_number,
    fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag,
    carries:special_teams_tds, contains(".rush"), contains(".rec"))

19.4.8 Split into Test and Training Data

seasonalData_lag_qb_all <- seasonalData_lag_subsetQB
seasonalData_lag_rb_all <- seasonalData_lag_subsetRB
seasonalData_lag_wr_all <- seasonalData_lag_subsetWR
seasonalData_lag_te_all <- seasonalData_lag_subsetTE

set.seed(52242) # for reproducibility (to keep the same train/holdout players)

activeQBs <- unique(seasonalData_lag_qb_all$gsis_id[which(seasonalData_lag_qb_all$season == max(seasonalData_lag_qb_all$season, na.rm = TRUE))])
retiredQBs <- unique(seasonalData_lag_qb_all$gsis_id[which(seasonalData_lag_qb_all$gsis_id %ni% activeQBs)])
numQBs <- length(unique(seasonalData_lag_qb_all$gsis_id))
qbHoldoutIDs <- sample(retiredQBs, size = ceiling(.2 * numQBs)) # holdout 20% of players

activeRBs <- unique(seasonalData_lag_rb_all$gsis_id[which(seasonalData_lag_rb_all$season == max(seasonalData_lag_rb_all$season, na.rm = TRUE))])
retiredRBs <- unique(seasonalData_lag_rb_all$gsis_id[which(seasonalData_lag_rb_all$gsis_id %ni% activeRBs)])
numRBs <- length(unique(seasonalData_lag_rb_all$gsis_id))
rbHoldoutIDs <- sample(retiredRBs, size = ceiling(.2 * numRBs)) # holdout 20% of players

set.seed(52242) # for reproducibility (to keep the same train/holdout players); added here to prevent a downstream error with predict.missRanger() due to missingness; this suggests that an error can arise from including a player in the holdout sample who has missingness in particular variables; would be good to identify which player(s) in the holdout sample evoke that error to identify the kinds of missingness that yield the error

activeWRs <- unique(seasonalData_lag_wr_all$gsis_id[which(seasonalData_lag_wr_all$season == max(seasonalData_lag_wr_all$season, na.rm = TRUE))])
retiredWRs <- unique(seasonalData_lag_wr_all$gsis_id[which(seasonalData_lag_wr_all$gsis_id %ni% activeWRs)])
numWRs <- length(unique(seasonalData_lag_wr_all$gsis_id))
wrHoldoutIDs <- sample(retiredWRs, size = ceiling(.2 * numWRs)) # holdout 20% of players

activeTEs <- unique(seasonalData_lag_te_all$gsis_id[which(seasonalData_lag_te_all$season == max(seasonalData_lag_te_all$season, na.rm = TRUE))])
retiredTEs <- unique(seasonalData_lag_te_all$gsis_id[which(seasonalData_lag_te_all$gsis_id %ni% activeTEs)])
numTEs <- length(unique(seasonalData_lag_te_all$gsis_id))
teHoldoutIDs <- sample(retiredTEs, size = ceiling(.2 * numTEs)) # holdout 20% of players
  
seasonalData_lag_qb_train <- seasonalData_lag_qb_all %>% 
  filter(gsis_id %ni% qbHoldoutIDs)
seasonalData_lag_qb_test <- seasonalData_lag_qb_all %>% 
  filter(gsis_id %in% qbHoldoutIDs)

seasonalData_lag_rb_train <- seasonalData_lag_rb_all %>% 
  filter(gsis_id %ni% rbHoldoutIDs)
seasonalData_lag_rb_test <- seasonalData_lag_rb_all %>% 
  filter(gsis_id %in% rbHoldoutIDs)

seasonalData_lag_wr_train <- seasonalData_lag_wr_all %>% 
  filter(gsis_id %ni% wrHoldoutIDs)
seasonalData_lag_wr_test <- seasonalData_lag_wr_all %>% 
  filter(gsis_id %in% wrHoldoutIDs)

seasonalData_lag_te_train <- seasonalData_lag_te_all %>% 
  filter(gsis_id %ni% teHoldoutIDs)
seasonalData_lag_te_test <- seasonalData_lag_te_all %>% 
  filter(gsis_id %in% teHoldoutIDs)

19.4.9 Impute the Missing Data

Here is a vignette demonstrating how to impute missing data using missForest(): https://rpubs.com/lmorgan95/MissForest (archived at: https://perma.cc/6GB4-2E22). Below, we impute the training data (and all data) separately by position. We then use the imputed training data to make out-of-sample predictions to fill in the missing data for the testing data. We do not want to impute the training and testing data together so that we can keep them separate for the purposes of cross-validation. However, we impute all data (training and test data together) for purposes of making out-of-sample predictions from the machine learning models to predict players’ performance next season (when actuals are not yet available for evaluating their accuracy). To impute data, we use the missRanger package (Mayer, 2024).

Note 19.1: Impute missing data for machine learning

Note: the following code takes a while to run.

# QBs
seasonalData_lag_qb_all_imp <- missRanger::missRanger(
  seasonalData_lag_qb_all,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        fantasy_points, fantasy_points_ppr, special_teams_tds, passing_epa, pacr, rushing_epa, fantasyPoints_lag, passing_cpoe, rookie_year, draft_number, gs, pass_attempts.pass, throwaways.pass, spikes.pass, drops.pass, bad_throws.pass, times_blitzed.pass, times_hurried.pass, times_hit.pass, times_pressured.pass, batted_balls.pass, on_tgt_throws.pass, rpo_plays.pass, rpo_yards.pass, rpo_pass_att.pass, rpo_pass_yards.pass, rpo_rush_att.pass, rpo_rush_yards.pass, pa_pass_att.pass, pa_pass_yards.pass, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, drop_pct.pass, bad_throw_pct.pass, on_tgt_pct.pass, pressure_pct.pass, ybc_att.rush, yac_att.rush, pocket_time.pass
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, completions, attempts, passing_yards, passing_tds, passing_interceptions, sacks_suffered, sack_yards_lost, sack_fumbles, sack_fumbles_lost, passing_air_yards, passing_yards_after_catch, passing_first_downs, passing_epa, passing_cpoe, passing_2pt_conversions, pacr, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, special_teams_tds, pocket_time.pass, pass_attempts.pass, throwaways.pass, spikes.pass, drops.pass, bad_throws.pass, times_blitzed.pass, times_hurried.pass, times_hit.pass, times_pressured.pass, batted_balls.pass, on_tgt_throws.pass, rpo_plays.pass, rpo_yards.pass, rpo_pass_att.pass, rpo_pass_yards.pass, rpo_rush_att.pass, rpo_rush_yards.pass, pa_pass_att.pass, pa_pass_yards.pass, drop_pct.pass, bad_throw_pct.pass, on_tgt_pct.pass, pressure_pct.pass, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush

    fntsy_  fnts__  spcl__  pssng_p pacr    rshng_  fntsP_  pssng_c rok_yr  drft_n  gs  pss_t.  thrww.  spks.p  drps.p  bd_th.  tms_b.  tms_hr. tms_ht. tms_p.  bttd_.  on_tgt_t.   rp_pl.  rp_yr.  rp_pss_t.   rp_pss_y.   rp_rsh_t.   rp_rsh_y.   p_pss_t.    p_pss_y.    att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_t.  att_b.  drp_p.  bd_t_.  on_tgt_p.   prss_.  ybc_t.  yc_tt.  pckt_.
iter 1: 0.0054  0.0024  0.7924  0.1919  0.7612  0.3628  0.4789  0.4133  0.0224  0.5216  0.0271  0.0134  0.3024  0.7659  0.1304  0.0541  0.0758  0.1759  0.1820  0.0370  0.3238  0.0291  0.2952  0.1812  0.0885  0.0867  0.2627  0.2563  0.1093  0.0902  0.0580  0.0645  0.1732  0.0524  0.0578  0.1795  0.3524  0.3428  0.7447  0.5158  0.0824  0.6803  0.3529  0.5758  0.8111  
iter 2: 0.0044  0.0048  0.8304  0.2002  0.7926  0.3736  0.4801  0.4289  0.0488  0.6139  0.0188  0.0090  0.2883  0.7481  0.0764  0.0385  0.0718  0.1231  0.1329  0.0337  0.2760  0.0113  0.0548  0.0814  0.0765  0.0990  0.1989  0.2841  0.0707  0.0952  0.0396  0.0386  0.1606  0.0492  0.0525  0.1220  0.2541  0.3556  0.7468  0.4937  0.0827  0.6610  0.3465  0.5796  0.8134  
iter 3: 0.0049  0.0046  0.8690  0.1986  0.7810  0.3641  0.4774  0.4360  0.0528  0.6123  0.0188  0.0088  0.2867  0.7538  0.0767  0.0393  0.0734  0.1261  0.1374  0.0343  0.2741  0.0119  0.0524  0.0816  0.0748  0.1008  0.2184  0.2811  0.0691  0.0926  0.0389  0.0413  0.1640  0.0511  0.0585  0.1255  0.2510  0.3609  0.7477  0.5108  0.0858  0.6426  0.3588  0.5734  0.8300  

seasonalData_lag_qb_all_imp

missRanger object. Extract imputed data via $data
- best iteration: 2 
- best average OOB imputation error: 0.2524825 

data_all_qb <- seasonalData_lag_qb_all_imp$data
data_all_qb_matrix <- data_all_qb %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()
newData_qb <- data_all_qb %>% 
  filter(season == max(season, na.rm = TRUE)) %>% 
  select(-fantasyPoints_lag)
newData_qb_matrix <- data_all_qb_matrix[
  data_all_qb_matrix[, "season"] == max(data_all_qb_matrix[, "season"], na.rm = TRUE), # keep only rows with the most recent season
  , # all columns
  drop = FALSE]

dropCol_qb <- which(colnames(newData_qb_matrix) == "fantasyPoints_lag")
newData_qb_matrix <- newData_qb_matrix[, -dropCol_qb, drop = FALSE]

seasonalData_lag_qb_train_imp <- missRanger::missRanger(
  seasonalData_lag_qb_train,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        fantasy_points, fantasy_points_ppr, special_teams_tds, passing_epa, pacr, rushing_epa, fantasyPoints_lag, passing_cpoe, rookie_year, draft_number, gs, pass_attempts.pass, throwaways.pass, spikes.pass, drops.pass, bad_throws.pass, times_blitzed.pass, times_hurried.pass, times_hit.pass, times_pressured.pass, batted_balls.pass, on_tgt_throws.pass, rpo_plays.pass, rpo_yards.pass, rpo_pass_att.pass, rpo_pass_yards.pass, rpo_rush_att.pass, rpo_rush_yards.pass, pa_pass_att.pass, pa_pass_yards.pass, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, drop_pct.pass, bad_throw_pct.pass, on_tgt_pct.pass, pressure_pct.pass, ybc_att.rush, yac_att.rush, pocket_time.pass
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, completions, attempts, passing_yards, passing_tds, passing_interceptions, sacks_suffered, sack_yards_lost, sack_fumbles, sack_fumbles_lost, passing_air_yards, passing_yards_after_catch, passing_first_downs, passing_epa, passing_cpoe, passing_2pt_conversions, pacr, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, special_teams_tds, pocket_time.pass, pass_attempts.pass, throwaways.pass, spikes.pass, drops.pass, bad_throws.pass, times_blitzed.pass, times_hurried.pass, times_hit.pass, times_pressured.pass, batted_balls.pass, on_tgt_throws.pass, rpo_plays.pass, rpo_yards.pass, rpo_pass_att.pass, rpo_pass_yards.pass, rpo_rush_att.pass, rpo_rush_yards.pass, pa_pass_att.pass, pa_pass_yards.pass, drop_pct.pass, bad_throw_pct.pass, on_tgt_pct.pass, pressure_pct.pass, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush

    fntsy_  fnts__  spcl__  pssng_p pacr    rshng_  fntsP_  pssng_c rok_yr  drft_n  gs  pss_t.  thrww.  spks.p  drps.p  bd_th.  tms_b.  tms_hr. tms_ht. tms_p.  bttd_.  on_tgt_t.   rp_pl.  rp_yr.  rp_pss_t.   rp_pss_y.   rp_rsh_t.   rp_rsh_y.   p_pss_t.    p_pss_y.    att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_t.  att_b.  drp_p.  bd_t_.  on_tgt_p.   prss_.  ybc_t.  yc_tt.  pckt_.
iter 1: 0.0061  0.0028  0.8162  0.1897  0.5083  0.3633  0.4726  0.4456  0.0242  0.4723  0.0283  0.0141  0.2939  0.7728  0.1343  0.0558  0.0744  0.1757  0.1818  0.0381  0.3288  0.0351  0.2921  0.1846  0.0860  0.0894  0.2737  0.2661  0.1127  0.0900  0.0586  0.0644  0.1800  0.0574  0.0639  0.1792  0.3570  0.3486  0.7646  0.5313  0.0868  0.7084  0.3533  0.5933  0.8466  
iter 2: 0.0052  0.0052  0.8304  0.1937  0.5621  0.3715  0.4614  0.4586  0.0505  0.5647  0.0192  0.0092  0.2953  0.7530  0.0800  0.0393  0.0725  0.1170  0.1355  0.0343  0.2771  0.0121  0.0555  0.0731  0.0713  0.0979  0.2073  0.2943  0.0698  0.0911  0.0416  0.0399  0.1683  0.0527  0.0577  0.1262  0.2474  0.3582  0.7719  0.5165  0.0900  0.6862  0.3642  0.5926  0.8400  
iter 3: 0.0053  0.0051  0.8261  0.2008  0.5551  0.3571  0.4727  0.4410  0.0551  0.5658  0.0188  0.0092  0.2859  0.7460  0.0807  0.0402  0.0739  0.1202  0.1393  0.0351  0.2808  0.0114  0.0595  0.0705  0.0775  0.1051  0.2163  0.2935  0.0718  0.0921  0.0426  0.0400  0.1719  0.0535  0.0534  0.1225  0.2498  0.3484  0.7502  0.5100  0.0884  0.6609  0.3672  0.5852  0.8440  
iter 4: 0.0054  0.0051  0.6928  0.1979  0.5598  0.3732  0.4771  0.4349  0.0506  0.5691  0.0189  0.0085  0.2891  0.7456  0.0785  0.0395  0.0737  0.1210  0.1353  0.0335  0.2836  0.0117  0.0566  0.0778  0.0743  0.1055  0.2131  0.2964  0.0697  0.0912  0.0396  0.0395  0.1611  0.0531  0.0597  0.1258  0.2600  0.3560  0.8062  0.5032  0.0973  0.6739  0.3698  0.5875  0.8485  
iter 5: 0.0052  0.0055  0.8355  0.1965  0.5664  0.3710  0.4743  0.4604  0.0520  0.5598  0.0193  0.0091  0.2852  0.7474  0.0800  0.0405  0.0722  0.1213  0.1366  0.0344  0.2788  0.0118  0.0555  0.0756  0.0746  0.0986  0.2190  0.2765  0.0695  0.0932  0.0390  0.0425  0.1650  0.0509  0.0576  0.1305  0.2556  0.3509  0.7738  0.5051  0.0969  0.6902  0.3640  0.6007  0.8326  

seasonalData_lag_qb_train_imp

missRanger object. Extract imputed data via $data
- best iteration: 4 
- best average OOB imputation error: 0.2482278 

data_train_qb <- seasonalData_lag_qb_train_imp$data
data_train_qb_matrix <- data_train_qb %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

seasonalData_lag_qb_test_imp <- predict(
  object = seasonalData_lag_qb_train_imp,
  newdata = seasonalData_lag_qb_test,
  seed = 52242)

data_test_qb <- seasonalData_lag_qb_test_imp
data_test_qb_matrix <- data_test_qb %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

# RBs
seasonalData_lag_rb_all_imp <- missRanger::missRanger(
  seasonalData_lag_rb_all,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        games, ageCentered20, ageCentered20Quadratic, fantasy_points, fantasy_points_ppr, fantasyPoints, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_2pt_conversions, special_teams_tds, years_of_experience, rushing_epa, air_yards_share, receiving_epa, racr, target_share, wopr, fantasyPoints_lag, rookie_year, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, ybc_att.rush, yac_att.rush, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec

    games   agCn20  agC20Q  fntsy_  fnts__  fntsyP  carris  rshng_y rshng_t rshng_f rshng_fm_   rshng_fr_   rsh_2_  rcptns  targts  rcvng_y rcvng_t rcvng_f rcvng_fm_   rcvng_r_    rcv___  rcvng_fr_   rcv_2_  spcl__  yrs_f_  rshng_p ar_yr_  rcvng_p racr    trgt_s  wopr    fntsP_  rok_yr  drft_n  gs  att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_tkl.rs  att_b.  tgt.rc  rec.rc  yds.rc  td.rec  x1d.rc  ybc.rc  yac.rc  brk_tkl.rc  drp.rc  int.rc  ybc_t.  yc_tt.  adt.rc  rat.rc  drp_p.  rc_br.  ybc_r.  yc_r.r
iter 1: 0.8865  0.0057  0.0031  0.4544  0.0178  0.0032  0.0745  0.0233  0.1462  0.4895  0.2594  0.0295  0.9849  0.0690  0.0666  0.0534  0.4327  0.8626  0.4824  0.6841  0.0322  0.0614  1.0171  0.8263  0.1817  0.4512  0.3321  0.3894  0.5211  0.4549  0.1817  0.5440  0.0197  0.5999  0.1700  0.0244  0.0222  0.0792  0.0297  0.0527  0.0520  0.2134  0.3431  0.0252  0.0180  0.0257  0.1634  0.0437  0.3108  0.0217  0.3925  0.4610  0.6941  0.4880  0.5402  0.2670  0.2026  0.3482  0.1596  0.2698  0.3637  
iter 2: 0.2755  0.0162  0.0207  0.0063  0.0037  0.0044  0.0161  0.0148  0.0912  0.2524  0.2898  0.0248  0.9832  0.0273  0.0444  0.0233  0.2065  0.4600  0.4891  0.1285  0.0332  0.0457  1.0175  0.8566  0.1824  0.4212  0.2329  0.3099  0.5605  0.2569  0.1742  0.5373  0.0424  0.6377  0.1653  0.0167  0.0123  0.0859  0.0302  0.0367  0.0349  0.1030  0.3689  0.0144  0.0159  0.0195  0.1403  0.0434  0.1549  0.0190  0.3840  0.1050  0.5453  0.4882  0.5616  0.2472  0.1953  0.1525  0.1687  0.2595  0.3619  
iter 3: 0.2744  0.0163  0.0231  0.0062  0.0038  0.0047  0.0152  0.0137  0.0980  0.2601  0.2906  0.0244  0.9800  0.0265  0.0347  0.0231  0.2101  0.4638  0.4954  0.1284  0.0283  0.0458  1.0114  0.8731  0.1818  0.4117  0.2278  0.3037  0.5699  0.2052  0.1800  0.5389  0.0400  0.6423  0.1624  0.0166  0.0124  0.0893  0.0306  0.0374  0.0356  0.1074  0.3628  0.0144  0.0163  0.0187  0.1390  0.0463  0.1583  0.0190  0.3882  0.1062  0.5642  0.4796  0.5570  0.2380  0.1935  0.1586  0.1588  0.2625  0.3648  
iter 4: 0.2776  0.0169  0.0220  0.0063  0.0038  0.0045  0.0151  0.0138  0.0979  0.2584  0.2846  0.0243  0.9782  0.0263  0.0281  0.0221  0.1968  0.4594  0.4817  0.1267  0.0290  0.0462  1.0104  0.8614  0.1854  0.4216  0.2333  0.3004  0.5467  0.1917  0.1815  0.5353  0.0443  0.6503  0.1657  0.0166  0.0121  0.0905  0.0313  0.0378  0.0357  0.1041  0.3437  0.0155  0.0159  0.0185  0.1405  0.0441  0.1613  0.0196  0.3816  0.1117  0.5682  0.5011  0.5585  0.2421  0.1975  0.1520  0.1770  0.2650  0.3647  
iter 5: 0.2752  0.0163  0.0226  0.0063  0.0038  0.0045  0.0158  0.0138  0.1015  0.2614  0.2857  0.0242  0.9740  0.0250  0.0303  0.0218  0.2004  0.4607  0.4810  0.1167  0.0285  0.0449  1.0077  0.8658  0.1835  0.4182  0.2170  0.2995  0.5690  0.2010  0.1794  0.5375  0.0385  0.6487  0.1652  0.0166  0.0124  0.0878  0.0306  0.0368  0.0353  0.1069  0.3539  0.0154  0.0159  0.0193  0.1409  0.0447  0.1598  0.0205  0.3873  0.1062  0.5583  0.4895  0.5501  0.2418  0.1979  0.1713  0.1726  0.2625  0.3596  
iter 6: 0.2760  0.0158  0.0223  0.0063  0.0037  0.0046  0.0150  0.0144  0.0982  0.2568  0.2816  0.0238  0.9810  0.0253  0.0273  0.0223  0.2141  0.4606  0.4881  0.1386  0.0300  0.0457  1.0174  0.8605  0.1821  0.4188  0.2263  0.2985  0.5497  0.1779  0.1536  0.5388  0.0389  0.6422  0.1668  0.0162  0.0119  0.0897  0.0305  0.0376  0.0356  0.1066  0.3529  0.0149  0.0159  0.0196  0.1446  0.0450  0.1585  0.0197  0.3857  0.1001  0.5607  0.4948  0.5478  0.2487  0.1945  0.1438  0.1543  0.2568  0.3612  
iter 7: 0.2748  0.0158  0.0212  0.0064  0.0039  0.0047  0.0149  0.0141  0.0986  0.2611  0.2877  0.0241  0.9755  0.0253  0.0310  0.0223  0.2163  0.4553  0.4885  0.1335  0.0293  0.0456  1.0096  0.8575  0.1821  0.4236  0.2203  0.2998  0.5510  0.2107  0.1797  0.5354  0.0416  0.6395  0.1646  0.0166  0.0117  0.0895  0.0310  0.0371  0.0361  0.1073  0.3547  0.0154  0.0156  0.0193  0.1410  0.0449  0.1628  0.0201  0.3892  0.1076  0.5609  0.4946  0.5643  0.2392  0.1899  0.1540  0.1423  0.2667  0.3603  

seasonalData_lag_rb_all_imp

missRanger object. Extract imputed data via $data
- best iteration: 6 
- best average OOB imputation error: 0.2175486 

data_all_rb <- seasonalData_lag_rb_all_imp$data
data_all_rb_matrix <- data_all_rb %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()
newData_rb <- data_all_rb %>% 
  filter(season == max(season, na.rm = TRUE)) %>% 
  select(-fantasyPoints_lag)
newData_rb_matrix <- data_all_rb_matrix[
  data_all_rb_matrix[, "season"] == max(data_all_rb_matrix[, "season"], na.rm = TRUE), # keep only rows with the most recent season
  , # all columns
  drop = FALSE]

dropCol_rb <- which(colnames(newData_rb_matrix) == "fantasyPoints_lag")
newData_rb_matrix <- newData_rb_matrix[, -dropCol_rb, drop = FALSE]

seasonalData_lag_rb_train_imp <- missRanger::missRanger(
  seasonalData_lag_rb_train,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        games, ageCentered20, ageCentered20Quadratic, fantasy_points, fantasy_points_ppr, fantasyPoints, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_2pt_conversions, special_teams_tds, years_of_experience, rushing_epa, air_yards_share, receiving_epa, racr, target_share, wopr, fantasyPoints_lag, rookie_year, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, ybc_att.rush, yac_att.rush, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec

    games   agCn20  agC20Q  fntsy_  fnts__  fntsyP  carris  rshng_y rshng_t rshng_f rshng_fm_   rshng_fr_   rsh_2_  rcptns  targts  rcvng_y rcvng_t rcvng_f rcvng_fm_   rcvng_r_    rcv___  rcvng_fr_   rcv_2_  spcl__  yrs_f_  rshng_p ar_yr_  rcvng_p racr    trgt_s  wopr    fntsP_  rok_yr  drft_n  gs  att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_tkl.rs  att_b.  tgt.rc  rec.rc  yds.rc  td.rec  x1d.rc  ybc.rc  yac.rc  brk_tkl.rc  drp.rc  int.rc  ybc_t.  yc_tt.  adt.rc  rat.rc  drp_p.  rc_br.  ybc_r.  yc_r.r
iter 1: 0.8759  0.0072  0.0036  0.4578  0.0178  0.0035  0.0736  0.0229  0.1524  0.4776  0.2679  0.0288  0.9965  0.0749  0.0744  0.0553  0.4578  0.8604  0.4998  0.6821  0.0360  0.0639  1.0042  0.8380  0.1806  0.4662  0.3419  0.3961  0.5595  0.4715  0.1968  0.5338  0.0246  0.5882  0.1726  0.0265  0.0235  0.0849  0.0311  0.0550  0.0521  0.2131  0.3689  0.0281  0.0197  0.0286  0.1742  0.0463  0.3114  0.0229  0.3942  0.4806  0.7239  0.5199  0.5631  0.2865  0.2195  0.3630  0.2052  0.2596  0.4091  
iter 2: 0.2745  0.0177  0.0266  0.0067  0.0041  0.0049  0.0169  0.0154  0.1017  0.2590  0.2956  0.0237  0.9814  0.0286  0.0522  0.0240  0.2187  0.4582  0.4919  0.1541  0.0362  0.0475  1.0075  0.8811  0.1822  0.4481  0.2377  0.3184  0.6116  0.2628  0.2007  0.5254  0.0473  0.6411  0.1653  0.0179  0.0132  0.0940  0.0325  0.0392  0.0375  0.1057  0.3678  0.0161  0.0169  0.0196  0.1510  0.0484  0.1521  0.0202  0.3941  0.1035  0.5567  0.5120  0.5666  0.2466  0.2087  0.1733  0.1699  0.2524  0.4066  
iter 3: 0.2766  0.0190  0.0273  0.0067  0.0041  0.0048  0.0159  0.0149  0.0971  0.2615  0.2952  0.0245  0.9668  0.0278  0.0409  0.0240  0.2180  0.4648  0.4931  0.1319  0.0350  0.0495  1.0128  0.8907  0.1820  0.4366  0.2459  0.3124  0.6236  0.2555  0.2114  0.5276  0.0438  0.6314  0.1658  0.0175  0.0122  0.0899  0.0319  0.0386  0.0386  0.1100  0.3783  0.0155  0.0165  0.0194  0.1477  0.0474  0.1499  0.0194  0.3929  0.1121  0.5761  0.5245  0.5651  0.2490  0.2103  0.1767  0.1817  0.2658  0.4106  

seasonalData_lag_rb_train_imp

missRanger object. Extract imputed data via $data
- best iteration: 2 
- best average OOB imputation error: 0.226086 

data_train_rb <- seasonalData_lag_rb_train_imp$data
data_train_rb_matrix <- data_train_rb %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

seasonalData_lag_rb_test_imp <- predict(
  object = seasonalData_lag_rb_train_imp,
  newdata = seasonalData_lag_rb_test,
  seed = 52242)

data_test_rb <- seasonalData_lag_rb_test_imp
data_test_rb_matrix <- data_test_rb %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

# WRs
seasonalData_lag_wr_all_imp <- missRanger::missRanger(
  seasonalData_lag_wr_all,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        fantasy_points, fantasy_points_ppr, special_teams_tds, years_of_experience, receiving_epa, racr, air_yards_share, target_share, wopr, fantasyPoints_lag, rookie_year, rushing_epa, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec, ybc_att.rush, yac_att.rush
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec

    fntsy_  fnts__  spcl__  yrs_f_  rcvng_  racr    ar_yr_  trgt_s  wopr    fntsP_  rok_yr  rshng_  drft_n  gs  att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_tkl.rs  att_b.  tgt.rc  rec.rc  yds.rc  td.rec  x1d.rc  ybc.rc  yac.rc  brk_tkl.rc  drp.rc  int.rc  adt.rc  rat.rc  drp_p.  rc_br.  ybc_r.  yc_r.r  ybc_t.  yc_tt.
iter 1: 0.0061  0.0010  0.7104  0.1566  0.1040  0.8131  0.1013  0.1722  0.0402  0.4890  0.0150  0.3811  0.6654  0.1459  0.1184  0.0898  0.2353  0.1234  0.0966  0.2670  0.6383  0.3084  0.0198  0.0136  0.0151  0.0671  0.0135  0.0268  0.0442  0.4465  0.4320  0.4674  0.2961  0.1410  0.3819  0.1840  0.2251  0.3929  0.2568  0.4760  
iter 2: 0.0058  0.0019  0.7826  0.1601  0.0835  0.7518  0.0607  0.0930  0.0452  0.4939  0.0296  0.3301  0.6843  0.1440  0.0851  0.0600  0.2638  0.1161  0.0708  0.1804  0.3103  0.3223  0.0109  0.0108  0.0096  0.0719  0.0139  0.0200  0.0318  0.4476  0.0778  0.3692  0.2401  0.1448  0.1629  0.1601  0.2261  0.3793  0.2536  0.4775  
iter 3: 0.0061  0.0019  0.7857  0.1593  0.0829  0.7421  0.0580  0.0986  0.0481  0.4946  0.0318  0.3334  0.6890  0.1430  0.0823  0.0604  0.2595  0.1177  0.0728  0.1802  0.3077  0.3194  0.0109  0.0114  0.0095  0.0724  0.0133  0.0199  0.0312  0.4411  0.0767  0.3687  0.2369  0.1455  0.1530  0.1660  0.2169  0.3878  0.2466  0.4716  
iter 4: 0.0060  0.0018  0.7874  0.1604  0.0832  0.7394  0.0591  0.0940  0.0479  0.4926  0.0301  0.3317  0.6896  0.1434  0.0863  0.0601  0.2562  0.1227  0.0711  0.1900  0.3089  0.3194  0.0105  0.0112  0.0095  0.0707  0.0140  0.0202  0.0318  0.4447  0.0784  0.3674  0.2339  0.1423  0.1592  0.1700  0.2254  0.3886  0.2552  0.4662  

seasonalData_lag_wr_all_imp

missRanger object. Extract imputed data via $data
- best iteration: 3 
- best average OOB imputation error: 0.203846 

data_all_wr <- seasonalData_lag_wr_all_imp$data
data_all_wr_matrix <- data_all_wr %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()
newData_wr <- data_all_wr %>% 
  filter(season == max(season, na.rm = TRUE)) %>% 
  select(-fantasyPoints_lag)
newData_wr_matrix <- data_all_wr_matrix[
  data_all_wr_matrix[, "season"] == max(data_all_wr_matrix[, "season"], na.rm = TRUE), # keep only rows with the most recent season
  , # all columns
  drop = FALSE]

dropCol_wr <- which(colnames(newData_wr_matrix) == "fantasyPoints_lag")
newData_wr_matrix <- newData_wr_matrix[, -dropCol_wr, drop = FALSE]

seasonalData_lag_wr_train_imp <- missRanger::missRanger(
  seasonalData_lag_wr_train,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        fantasy_points, fantasy_points_ppr, special_teams_tds, years_of_experience, receiving_epa, racr, air_yards_share, target_share, wopr, fantasyPoints_lag, rookie_year, rushing_epa, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec, ybc_att.rush, yac_att.rush
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec

    fntsy_  fnts__  spcl__  yrs_f_  rcvng_  racr    ar_yr_  trgt_s  wopr    fntsP_  rok_yr  rshng_  drft_n  gs  att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_tkl.rs  att_b.  tgt.rc  rec.rc  yds.rc  td.rec  x1d.rc  ybc.rc  yac.rc  brk_tkl.rc  drp.rc  int.rc  adt.rc  rat.rc  drp_p.  rc_br.  ybc_r.  yc_r.r  ybc_t.  yc_tt.
iter 1: 0.0064  0.0010  0.7029  0.1611  0.1089  0.8443  0.1021  0.1643  0.0427  0.4935  0.0173  0.3461  0.6788  0.1427  0.1364  0.0993  0.2403  0.1243  0.0979  0.2745  0.6190  0.3171  0.0201  0.0147  0.0159  0.0734  0.0140  0.0280  0.0454  0.4502  0.4439  0.4733  0.3088  0.1641  0.4547  0.2192  0.2439  0.4227  0.2921  0.5068  
iter 2: 0.0063  0.0020  0.7835  0.1630  0.0901  0.8044  0.0674  0.0936  0.0479  0.4930  0.0331  0.3235  0.7090  0.1417  0.0896  0.0659  0.2659  0.1273  0.0752  0.1920  0.3068  0.3225  0.0112  0.0116  0.0101  0.0753  0.0141  0.0210  0.0333  0.4431  0.0809  0.3676  0.2571  0.1617  0.1735  0.1797  0.2441  0.3996  0.2911  0.4923  
iter 3: 0.0063  0.0020  0.7710  0.1639  0.0881  0.7954  0.0646  0.0982  0.0515  0.4956  0.0338  0.3200  0.7088  0.1413  0.0900  0.0640  0.2565  0.1250  0.0735  0.1989  0.3082  0.3280  0.0114  0.0119  0.0096  0.0763  0.0141  0.0216  0.0326  0.4388  0.0807  0.3703  0.2582  0.1623  0.1657  0.2018  0.2375  0.4016  0.2838  0.4794  
iter 4: 0.0062  0.0020  0.7792  0.1625  0.0877  0.8043  0.0632  0.0919  0.0477  0.4963  0.0341  0.3239  0.7038  0.1420  0.0950  0.0653  0.2664  0.1309  0.0767  0.2025  0.2933  0.3076  0.0109  0.0119  0.0097  0.0745  0.0143  0.0217  0.0326  0.4432  0.0804  0.3688  0.2584  0.1605  0.1931  0.2013  0.2378  0.4119  0.2824  0.4860  

seasonalData_lag_wr_train_imp

missRanger object. Extract imputed data via $data
- best iteration: 3 
- best average OOB imputation error: 0.2110456 

data_train_wr <- seasonalData_lag_wr_train_imp$data
data_train_wr_matrix <- data_train_wr %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

seasonalData_lag_wr_test_imp <- predict(
  object = seasonalData_lag_wr_train_imp,
  newdata = seasonalData_lag_wr_test,
  seed = 52242)

data_test_wr <- seasonalData_lag_wr_test_imp
data_test_wr_matrix <- data_test_wr %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

# TEs
seasonalData_lag_te_all_imp <- missRanger::missRanger(
  seasonalData_lag_te_all,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        games, ageCentered20, ageCentered20Quadratic, fantasy_points, fantasy_points_ppr, fantasyPoints, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_2pt_conversions, special_teams_tds, years_of_experience, receiving_epa, racr, air_yards_share, target_share, wopr, fantasyPoints_lag, rookie_year, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec, rushing_epa, ybc_att.rush, yac_att.rush
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec

    games   agCn20  agC20Q  fntsy_  fnts__  fntsyP  carris  rshng_y rshng_t rshng_f rshng_fm_   rshng_fr_   rsh_2_  rcptns  targts  rcvng_y rcvng_t rcvng_f rcvng_fm_   rcvng_r_    rcv___  rcvng_fr_   rcv_2_  spcl__  yrs_f_  rcvng_p racr    ar_yr_  trgt_s  wopr    fntsP_  rok_yr  drft_n  gs  att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_tkl.rs  att_b.  tgt.rc  rec.rc  yds.rc  td.rec  x1d.rc  ybc.rc  yac.rc  brk_tkl.rc  drp.rc  int.rc  adt.rc  rat.rc  drp_p.  rc_br.  ybc_r.  yc_r.r  rshng_p ybc_t.  yc_tt.
iter 1: 0.8157  0.0061  0.0030  0.3406  0.0194  0.0039  0.5253  0.2259  0.2452  0.7083  0.6874  0.0802  1.1303  0.0281  0.0558  0.0255  0.0845  0.8134  0.4317  0.0655  0.0784  0.0253  0.9716  1.0271  0.1530  0.1689  0.6899  0.1092  0.4432  0.1004  0.4764  0.0180  0.6054  0.3846  0.0762  0.0832  0.1564  0.0618  0.0704  0.2123  0.3921  0.6733  0.0290  0.0207  0.0226  0.1012  0.0212  0.0420  0.0603  0.4332  0.4640  0.4996  0.2804  0.1667  0.3542  0.1652  0.2843  0.3948  0.3270  0.6620  0.7439  
iter 2: 0.1712  0.0175  0.0256  0.0106  0.0037  0.0055  0.1140  0.1113  0.0990  0.5369  0.7422  0.0852  1.1286  0.0193  0.0200  0.0128  0.0862  0.4248  0.4659  0.0206  0.0529  0.0217  0.9711  1.0114  0.1561  0.1397  0.6715  0.0766  0.1819  0.1085  0.4649  0.0366  0.6346  0.3880  0.0722  0.0728  0.1592  0.0680  0.0759  0.2034  0.3651  0.6811  0.0164  0.0158  0.0161  0.1080  0.0211  0.0327  0.0475  0.4342  0.1149  0.4173  0.2589  0.1742  0.1467  0.1531  0.2941  0.3851  0.3357  0.6846  0.7397  
iter 3: 0.1689  0.0170  0.0261  0.0114  0.0040  0.0056  0.1190  0.1155  0.0978  0.6088  0.7899  0.0945  1.1731  0.0195  0.0203  0.0132  0.0964  0.4270  0.4608  0.0202  0.0525  0.0214  0.9694  1.0265  0.1560  0.1380  0.6453  0.0751  0.1794  0.1204  0.4642  0.0364  0.6369  0.3853  0.0779  0.0786  0.1497  0.0569  0.0932  0.2027  0.4003  0.6633  0.0171  0.0164  0.0167  0.1049  0.0220  0.0335  0.0466  0.4371  0.1141  0.4304  0.2665  0.1775  0.1464  0.1537  0.2916  0.3720  0.3137  0.6640  0.7770  

seasonalData_lag_te_all_imp

missRanger object. Extract imputed data via $data
- best iteration: 2 
- best average OOB imputation error: 0.2477098 

data_all_te <- seasonalData_lag_te_all_imp$data
data_all_te_matrix <- data_all_te %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()
newData_te <- data_all_te %>% 
  filter(season == max(season, na.rm = TRUE)) %>% 
  select(-fantasyPoints_lag)
newData_te_matrix <- data_all_te_matrix[
  data_all_te_matrix[, "season"] == max(data_all_te_matrix[, "season"], na.rm = TRUE), # keep only rows with the most recent season
  , # all columns
  drop = FALSE]

dropCol_te <- which(colnames(newData_te_matrix) == "fantasyPoints_lag")
newData_te_matrix <- newData_te_matrix[, -dropCol_te, drop = FALSE]

seasonalData_lag_te_train_imp <- missRanger::missRanger(
  seasonalData_lag_te_train,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        games, years_of_experience, ageCentered20, ageCentered20Quadratic, fantasy_points, fantasy_points_ppr, fantasyPoints, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_2pt_conversions, special_teams_tds, receiving_epa, racr, air_yards_share, target_share, wopr, fantasyPoints_lag, rookie_year, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec, rushing_epa, ybc_att.rush, yac_att.rush
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec

    games   yrs_f_  agCn20  agC20Q  fntsy_  fnts__  fntsyP  carris  rshng_y rshng_t rshng_f rshng_fm_   rshng_fr_   rsh_2_  rcptns  targts  rcvng_y rcvng_t rcvng_f rcvng_fm_   rcvng_r_    rcv___  rcvng_fr_   rcv_2_  spcl__  rcvng_p racr    ar_yr_  trgt_s  wopr    fntsP_  rok_yr  drft_n  gs  att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_tkl.rs  att_b.  tgt.rc  rec.rc  yds.rc  td.rec  x1d.rc  ybc.rc  yac.rc  brk_tkl.rc  drp.rc  int.rc  adt.rc  rat.rc  drp_p.  rc_br.  ybc_r.  yc_r.r  rshng_p ybc_t.  yc_tt.
iter 1: 0.8094  0.1093  0.0070  0.0035  0.3272  0.0235  0.0052  0.2840  0.1426  0.2634  0.8628  0.7885  0.0924  1.1067  0.0298  0.0611  0.0249  0.0969  0.8177  0.4537  0.0650  0.0804  0.0249  0.9680  1.0235  0.1738  0.5438  0.0868  0.4123  0.1172  0.4597  0.0189  0.6057  0.3973  0.0877  0.0886  0.1516  0.0467  0.0593  0.2086  0.4018  0.6464  0.0296  0.0223  0.0237  0.1062  0.0207  0.0428  0.0579  0.4367  0.4700  0.4818  0.3045  0.1724  0.4722  0.2410  0.2693  0.4025  0.3943  0.4791  0.7521  
iter 2: 0.1728  0.1469  0.0179  0.0289  0.0104  0.0039  0.0051  0.0863  0.0763  0.1528  0.7880  0.9474  0.0849  1.0234  0.0193  0.0198  0.0137  0.0915  0.4327  0.4835  0.0238  0.0558  0.0221  0.9617  1.0376  0.1464  0.5141  0.0630  0.1827  0.1062  0.4562  0.0379  0.6361  0.3908  0.0641  0.0767  0.1425  0.0603  0.0747  0.1970  0.3903  0.6647  0.0182  0.0171  0.0165  0.1074  0.0226  0.0332  0.0503  0.4361  0.1170  0.4096  0.2673  0.1862  0.2255  0.2386  0.2793  0.4004  0.3648  0.5070  0.7621  
iter 3: 0.1713  0.1447  0.0195  0.0276  0.0104  0.0036  0.0051  0.0796  0.0889  0.1611  0.8505  0.9348  0.0904  1.0447  0.0196  0.0205  0.0134  0.0901  0.4465  0.4867  0.0233  0.0569  0.0222  0.9519  1.0103  0.1457  0.5062  0.0617  0.1698  0.1115  0.4530  0.0382  0.6521  0.3899  0.0665  0.0681  0.1457  0.0647  0.0866  0.2055  0.3919  0.6791  0.0169  0.0169  0.0168  0.1107  0.0213  0.0339  0.0500  0.4315  0.1200  0.4148  0.2745  0.1822  0.1947  0.2205  0.2778  0.4032  0.3639  0.4933  0.7741  

seasonalData_lag_te_train_imp

missRanger object. Extract imputed data via $data
- best iteration: 2 
- best average OOB imputation error: 0.2519559 

data_train_te <- seasonalData_lag_te_train_imp$data
data_train_te_matrix <- data_train_te %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

seasonalData_lag_te_test_imp <- predict(
  object = seasonalData_lag_te_train_imp,
  newdata = seasonalData_lag_te_test,
  seed = 52242)

data_test_te <- seasonalData_lag_te_test_imp
data_test_te_matrix <- data_test_te %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

19.5 Identify Cores for Parallel Processing

num_cores <- detectCores() - 1
num_true_cores <- parallel::detectCores(logical = FALSE) - 1

num_cores

[1] 4

19.6 Fitting the Traditional Regression Models

19.6.1 Regression with One Predictor

19.6.2 Regression with Multiple Predictors

19.7 Fitting the Machine Learning Models

19.7.1 Least Absolute Shrinkage and Selection Option (LASSO)

19.7.2 Ridge Regression

19.7.3 Elastic Net

19.7.4 Random Forest Machine Learning

19.7.4.1 Cross-Sectional Data

We use the caret package (Kuhn, 2024). We use the parallel (R-parallel?) and doParallel (Corporation & Weston, 2022) packages for parallel (faster) processing.

cl <- parallel::makeCluster(num_cores)
doParallel::registerDoParallel(cl)

set.seed(52242)

randomForest_qb <- caret::train(
  fantasyPoints_lag ~ ., # use all predictors
  data = seasonalData_lag_subsetQB_imp$ximp,
  method = "rf",
  trControl = trainControl(
    method = "cv",
    number = 10)) # 10-fold cross-validation

Error in eval(expr, p): object 'seasonalData_lag_subsetQB_imp' not found

randomForest_rb <- caret::train(
  fantasyPoints_lag ~ ., # use all predictors
  data = seasonalData_lag_subsetRB_imp$ximp,
  method = "rf",
  trControl = trainControl(
    method = "cv",
    number = 10)) # 10-fold cross-validation

Error in eval(expr, p): object 'seasonalData_lag_subsetRB_imp' not found

randomForest_wr <- caret::train(
  fantasyPoints_lag ~ ., # use all predictors
  data = seasonalData_lag_subsetWR_imp$ximp,
  method = "rf",
  trControl = trainControl(
    method = "cv",
    number = 10)) # 10-fold cross-validation

Error in eval(expr, p): object 'seasonalData_lag_subsetWR_imp' not found

randomForest_te <- caret::train(
  fantasyPoints_lag ~ ., # use all predictors
  data = seasonalData_lag_subsetTE_imp$ximp,
  method = "rf",
  trControl = trainControl(
    method = "cv",
    number = 10)) # 10-fold cross-validation

Error in eval(expr, p): object 'seasonalData_lag_subsetTE_imp' not found

stopCluster(cl)

print(randomForest_qb)

Error: object 'randomForest_qb' not found

print(randomForest_rb)

Error: object 'randomForest_rb' not found

print(randomForest_wr)

Error: object 'randomForest_wr' not found

print(randomForest_te)

Error: object 'randomForest_te' not found

newData_seasonalQB_imp$ximp$fantasyPoints_lag <- predict(
  randomForest_qb,
  newdata = newData_seasonalQB_imp$ximp
)

Error: object 'randomForest_qb' not found

newData_seasonalRB_imp$ximp$fantasyPoints_lag <- predict(
  randomForest_rb,
  newdata = newData_seasonalRB_imp$ximp
)

Error: object 'randomForest_rb' not found

newData_seasonalWR_imp$ximp$fantasyPoints_lag <- predict(
  randomForest_wr,
  newdata = newData_seasonalWR_imp$ximp
)

Error: object 'randomForest_wr' not found

newData_seasonalTE_imp$ximp$fantasyPoints_lag <- predict(
  randomForest_te,
  newdata = newData_seasonalTE_imp$ximp
)

Error: object 'randomForest_te' not found

newData_seasonalQB$fantasyPoints_lag <- newData_seasonalQB_imp$ximp$fantasyPoints_lag

Error: object 'newData_seasonalQB_imp' not found

newData_seasonalRB$fantasyPoints_lag <- newData_seasonalRB_imp$ximp$fantasyPoints_lag

Error: object 'newData_seasonalRB_imp' not found

newData_seasonalWR$fantasyPoints_lag <- newData_seasonalWR_imp$ximp$fantasyPoints_lag

Error: object 'newData_seasonalWR_imp' not found

newData_seasonalTE$fantasyPoints_lag <- newData_seasonalTE_imp$ximp$fantasyPoints_lag

Error: object 'newData_seasonalTE_imp' not found

newData_seasonalQB <- dplyr::left_join(
  newData_seasonalQB,
  newData_seasonal %>% select(gsis_id, player_display_name, team),
  by = "gsis_id"
)

Error: object 'newData_seasonalQB' not found

newData_seasonalRB <- dplyr::left_join(
  newData_seasonalRB,
  newData_seasonal %>% select(gsis_id, player_display_name, team),
  by = "gsis_id"
)

Error: object 'newData_seasonalRB' not found

newData_seasonalWR <- dplyr::left_join(
  newData_seasonalWR,
  newData_seasonal %>% select(gsis_id, player_display_name, team),
  by = "gsis_id"
)

Error: object 'newData_seasonalWR' not found

newData_seasonalTE <- dplyr::left_join(
  newData_seasonalTE,
  newData_seasonal %>% select(gsis_id, player_display_name, team),
  by = "gsis_id"
)

Error: object 'newData_seasonalTE' not found

newData_seasonalQB %>%
  arrange(-fantasyPoints_lag) %>% 
  select(gsis_id, player_display_name, fantasyPoints_lag)

Error: object 'newData_seasonalQB' not found

newData_seasonalRB %>%
  arrange(-fantasyPoints_lag) %>% 
  select(gsis_id, player_display_name, fantasyPoints_lag)

Error: object 'newData_seasonalRB' not found

newData_seasonalWR %>%
  arrange(-fantasyPoints_lag) %>% 
  select(gsis_id, player_display_name, fantasyPoints_lag)

Error: object 'newData_seasonalWR' not found

newData_seasonalTE %>%
  arrange(-fantasyPoints_lag) %>% 
  select(gsis_id, player_display_name, fantasyPoints_lag)

Error: object 'newData_seasonalTE' not found

19.7.4.2 Longitudinal Data

(Hu & Szymczak, 2023)

library("LongituRF")

smerf <- LongituRF::MERF(
  X = seasonalData_subsetQB_imp$ximp[,c("passing_epa")] %>% as.matrix(),
  Y = seasonalData_subsetQB$fantasyPoints_lag,
  Z = seasonalData_subsetQB_imp$ximp[,c("pacr")] %>% as.matrix(),
  id = seasonalData_subsetQB$gsis_id,
  time = seasonalData_subsetQB_imp$ximp[,c("ageCentered20")] %>% as.matrix(),
  ntree = 500,
  sto = "BM")

smerf$forest # the fitted random forest (obtained at the last iteration)
smerf$random_effects # the predicted random effects for each player
smerf$omega # the predicted stochastic processes
plot(smerf$Vraisemblance) # evolution of the log-likelihood
smerf$OOB # OOB error at each iteration

19.7.5 k-Fold Cross-Validation

19.7.6 Leave-One-Out (LOO) Cross-Validation

19.7.7 Combining Tree-Boosting with Mixed Models

To combine tree-boosting with mixed models, we use the gpboost package (gpboost?).

Adapted from here: https://towardsdatascience.com/mixed-effects-machine-learning-for-longitudinal-panel-data-with-gpboost-part-iii-523bb38effc

19.7.7.1 Process Data

If using a gamma distribution, it requires positive-only values:

#data_train_qb_matrix[,"fantasyPoints_lag"][data_train_qb_matrix[,"fantasyPoints_lag"] <= 0] <- 0.01

19.7.7.2 Specify Predictor Variables

pred_vars_qb <- data_train_qb_matrix %>% 
  as_tibble() %>% 
  select(-fantasyPoints_lag, -ageCentered20, ageCentered20Quadratic) %>% # -gsis_id
  names()

pred_vars_qb_categorical <- "gsis_id" # to specify categorical predictors

19.7.7.3 Specify General Model Options

model_likelihood <- "gaussian" # gamma
nrounds <- 2000

19.7.7.4 Identify Optimal Tuning Parameters

For identifying the optimal tuning parameters for boosting, we partition the training data into inner training data and validation data. We randomly split the training data into 80% inner training data and 20% held-out validation data. We then use the mean absolute error as our index of prediction accuracy on the held-out validation data.

# Partition training data into inner training data and validation data
ntrain_qb <- dim(data_train_qb_matrix)[1]

set.seed(52242)
valid_tune_idx_qb <- sample.int(ntrain_qb, as.integer(0.2*ntrain_qb)) # 

folds_qb <- list(valid_tune_idx_qb)

# Specify parameter grid, gp_model, and gpb.Dataset
param_grid_qb <- list(
  "learning_rate" = c(0.2, 0.1, 0.05, 0.01),
  "max_depth" = c(3, 5, 7),
  "min_data_in_leaf" = c(10, 50, 100),
  "lambda_l2" = c(0, 1, 5))

other_params_qb <- list(
  num_leaves = 2^6) # 2^n, where n is smaller than the largest max_depth

gp_model_qb <- gpboost::GPModel(
  group_data = data_train_qb_matrix[,"gsis_id"],
  likelihood = model_likelihood,
  group_rand_coef_data = cbind(
    data_train_qb_matrix[,"ageCentered20"],
    data_train_qb_matrix[,"ageCentered20Quadratic"]),
  ind_effect_group_rand_coef = c(1,1))

gp_data_qb <- gpboost::gpb.Dataset(
  data = data_train_qb_matrix[,pred_vars_qb],
  categorical_feature = pred_vars_qb_categorical,
  label = data_train_qb_matrix[,"fantasyPoints_lag"])

# Find optimal tuning parameters
opt_params_qb <- gpboost::gpb.grid.search.tune.parameters(
  param_grid = param_grid_qb,
  params = other_params_qb,
  num_try_random = NULL,
  folds = folds_qb,
  data = gp_data_qb,
  gp_model = gp_model_qb,
  nrounds = nrounds,
  early_stopping_rounds = 50,
  verbose_eval = 1,
  metric = "mae")

opt_params_qb

$best_params
$best_params$learning_rate
[1] 0.2

$best_params$max_depth
[1] 7

$best_params$min_data_in_leaf
[1] 10

$best_params$lambda_l2
[1] 0


$best_iter
[1] 2000

$best_score
[1] 64.71963

A learning rate of 1 is very high for boosting. Even if a learning rate of 1 did well in tuning, I use a lower learning rate (0.2) to avoid overfitting. I also added some light regularization (lambda_l2) for better generalization. I also set the maximum tree depth (max_depth) at 7 to capture up to 3-way interactions, and set the maximum number of terminal nodes (num_leaves) per tree at 2^5 (32). I set the minimum number of samples in any leaf (min_data_in_leaf) to be 50.

19.7.7.5 Specify Model and Tuning Parameters

gp_model_qb <- gpboost::GPModel(
  group_data = data_train_qb_matrix[,"gsis_id"],
  likelihood = model_likelihood,
  group_rand_coef_data = cbind(
    data_train_qb_matrix[,"ageCentered20"],
    data_train_qb_matrix[,"ageCentered20Quadratic"]),
  ind_effect_group_rand_coef = c(1,1))

gp_data_qb <- gpboost::gpb.Dataset(
  data = data_train_qb_matrix[,pred_vars_qb],
  categorical_feature = pred_vars_qb_categorical,
  label = data_train_qb_matrix[,"fantasyPoints_lag"])

params_qb <- list(
  learning_rate = 0.2, # 0.1,
  max_depth = 7, #3,
  min_data_in_leaf = 10, #50
  lambda_l2 = 0, # 1,
  num_leaves = 2^6, #2^5,
  num_threads = num_cores)

nrounds_qb <- 2000 # identify optimal number of trees through iteration and cross-validation

#gp_model_qb$set_optim_params(params = list(optimizer_cov = "nelder_mead")) # to speed up model estimation

19.7.7.6 Fit Model

gp_model_fit_qb <- gpboost::gpb.train(
  data = gp_data_qb,
  gp_model = gp_model_qb,
  nrounds = nrounds_qb,
  params = params_qb) # verbose = 0

[GPBoost] [Info] Total Bins 8709
[GPBoost] [Info] Number of data points in the train set: 1582, number of used features: 73
[GPBoost] [Info] [GPBoost with gaussian likelihood]: initscore=111.481871
[GPBoost] [Info] Start training from score 111.481871

summary(gp_model_qb) # Estimated random effects model

=====================================================
Covariance parameters (random effects):
                          Param.
Error_term             5157.8499
Group_1                6709.3113
Group_1_rand_coef_nb_1    4.6555
Group_1_rand_coef_nb_2    0.1018
=====================================================

19.7.7.7 Evaluate Accuracy of Model on Test Data

# Test Model on Test Data
pred_test_qb <- predict(
  gp_model_fit_qb,
  data = data_test_qb_matrix[,pred_vars_qb],
  group_data_pred = data_test_qb_matrix[,"gsis_id"],
  group_rand_coef_data_pred = cbind(
    data_test_qb_matrix[,"ageCentered20"],
    data_test_qb_matrix[,"ageCentered20Quadratic"]),
  predict_var = FALSE,
  pred_latent = FALSE)

y_pred_test_qb <- pred_test_qb[["response_mean"]]
cbind(y_pred_test_qb, data_test_qb_matrix[,"fantasyPoints_lag"])

       y_pred_test_qb       
  [1,]       110.9396 156.46
  [2,]       110.9396 130.18
  [3,]       110.1854   2.98
  [4,]       110.4828  24.84
  [5,]       110.4828  40.28
  [6,]       110.4828  10.58
  [7,]       110.4828   0.68
  [8,]       109.7286  25.08
  [9,]       109.7286   6.12
 [10,]       110.4828  17.00
 [11,]       110.4828  44.54
 [12,]       110.0504 152.30
 [13,]       110.1854  -0.10
 [14,]       109.7286 137.96
 [15,]       110.9396 154.78
 [16,]       118.2726   7.64
 [17,]       110.4828   6.10
 [18,]       109.7286 228.66
 [19,]       113.4060 207.44
 [20,]       112.9786  23.80
 [21,]       110.4828 263.06
 [22,]       112.9786 157.30
 [23,]       114.2201 174.48
 [24,]       114.3535 228.56
 [25,]       112.9786  75.36
 [26,]       110.4828   6.72
 [27,]       111.2378  75.06
 [28,]       110.4828 173.40
 [29,]       112.9786 161.88
 [30,]       112.9786  81.36
 [31,]       109.7286  19.86
 [32,]       110.4828  74.86
 [33,]       110.4828  48.92
 [34,]       110.4828  97.48
 [35,]       109.7286  32.84
 [36,]       110.4828  -0.40
 [37,]       118.7898 121.84
 [38,]       110.4828 197.76
 [39,]       112.9786   3.16
 [40,]       111.3433 104.68
 [41,]       110.4828  31.94
 [42,]       111.3433   4.06
 [43,]       109.7286   7.22
 [44,]       113.7814 350.52
 [45,]       111.3560 313.92
 [46,]       114.2201 259.06
 [47,]       118.1769 240.26
 [48,]       118.2726 123.14
 [49,]       110.4828  48.58
 [50,]       109.7286 103.06
 [51,]       110.4828 167.20
 [52,]       116.6921 175.58
 [53,]       111.5761  -0.20
 [54,]       109.7286  71.82
 [55,]       112.0433 244.56
 [56,]       113.4060 156.12
 [57,]       114.5369 222.18
 [58,]       110.2097  17.78
 [59,]       109.0526   1.54
 [60,]       110.4828 134.74
 [61,]       110.4828 182.74
 [62,]       114.1969 177.76
 [63,]       112.9786  14.66
 [64,]       109.7286  19.84
 [65,]       109.7286 150.30
 [66,]       109.7286  44.56
 [67,]       110.4828  40.26
 [68,]       109.7286  86.84
 [69,]       110.4828   5.46
 [70,]       109.7286  43.82
 [71,]       110.0504 303.70
 [72,]       119.5381 271.52
 [73,]       119.5381 235.56
 [74,]       110.0504 230.12
 [75,]       117.7914 310.10
 [76,]       112.9786 165.78
 [77,]       110.9396 201.68
 [78,]       111.5761 219.56
 [79,]       114.2201 255.66
 [80,]       112.9786 248.32
 [81,]       113.6054 193.18
 [82,]       112.9786  66.94
 [83,]       110.4828  44.54
 [84,]       110.4828  11.04
 [85,]       109.7286  67.98
 [86,]       109.7286   6.12
 [87,]       110.4828  12.52
 [88,]       109.7286  -0.20
 [89,]       109.7286  46.68
 [90,]       109.7286  -0.10
 [91,]       109.7286   9.26
 [92,]       110.4828  -0.06
 [93,]       109.7286   2.30
 [94,]       111.3433  75.88
 [95,]       110.9396 157.64
 [96,]       112.9786 218.42
 [97,]       112.9786 204.38
 [98,]       114.2201 178.82
 [99,]       111.5761 275.06
[100,]       114.9687 225.24
[101,]       114.2201 118.96
[102,]       114.6264  49.64
[103,]       109.7286  26.64
[104,]       109.7286  -0.10
[105,]       110.4828  18.02
[106,]       110.4983  35.82
[107,]       109.7286  -0.30
[108,]       109.6746  76.02
[109,]       109.7286   5.48
[110,]       110.4828   3.18
[111,]       110.4828 279.60
[112,]       109.7286  41.64
[113,]       118.2726 194.00
[114,]       105.2860 254.06
[115,]       117.7914  95.30
[116,]       110.4828 117.72
[117,]       114.6264  -0.10
[118,]       110.4828   3.00
[119,]       109.7286  25.82
[120,]       110.4828   2.68
[121,]       109.7286 115.54
[122,]       110.9396   0.20
[123,]       109.7286  -4.64
[124,]       109.7286  41.90
[125,]       110.4828   8.78
[126,]       110.4828 222.70
[127,]       112.9786 144.26
[128,]       110.1854 172.02
[129,]       110.9396  33.90
[130,]       109.7286 185.88
[131,]       114.2201 108.84
[132,]       110.4828 222.92
[133,]       116.0647  17.22
[134,]       109.7286   0.76
[135,]       109.7286   5.90
[136,]       110.4828   2.54
[137,]       109.7286  17.28
[138,]       110.4828  58.24
[139,]       109.7286 123.26
[140,]       110.9396  38.48
[141,]       109.7286  44.22
[142,]       110.4828  17.06
[143,]       110.4828   9.30
[144,]       110.4828   0.70
[145,]       108.1067  -0.30
[146,]       110.4828  11.16
[147,]       109.7286   7.86
[148,]       110.4828   5.62
[149,]       110.4828   1.26
[150,]       110.4828   3.12
[151,]       110.4828   0.02
[152,]       110.4828  51.52
[153,]       109.7286   0.66
[154,]       111.0211  80.12
[155,]       110.5121 156.14
[156,]       110.9396 103.18
[157,]       110.4828   3.50
[158,]       110.4828  86.94
[159,]       109.0526  -0.30
[160,]       110.4828   0.08
[161,]       110.4828  29.36
[162,]       113.8466 142.06
[163,]       111.5761 145.94
[164,]       110.4828 145.16
[165,]       110.4828  64.10
[166,]       110.4828 225.44
[167,]       114.2201  20.76
[168,]       110.4828   0.76
[169,]       110.4828  54.90
[170,]       110.4828   1.24
[171,]       109.7286   2.06
[172,]       110.4828 192.06
[173,]       109.6746   7.76
[174,]       110.4828 187.32
[175,]       116.2481 309.64
[176,]       114.2201 226.02
[177,]       114.2201 287.82
[178,]       113.4060  99.10
[179,]       110.4828 293.96
[180,]       114.2201 289.92
[181,]       113.5839 270.92
[182,]       112.9786 279.30
[183,]       114.2201  44.66
[184,]       110.4828   5.16
[185,]       110.4828   1.36
[186,]       110.4828  18.52
[187,]       110.4828   9.80
[188,]       110.4828 108.18
[189,]       110.4828  49.40
[190,]       110.4828  13.42
[191,]       109.6746 116.84
[192,]       110.4828 190.52
[193,]       114.2201 287.90
[194,]       111.8846 254.60
[195,]       112.9786 162.06
[196,]       116.6921 227.82
[197,]       112.9786 106.80
[198,]       110.4828   0.28
[199,]       110.4828  26.60
[200,]       110.4828   0.44
[201,]       110.4828   3.10
[202,]       110.4828  34.90
[203,]       110.4828  -0.40
[204,]       110.4828  20.94
[205,]       108.3542 228.48
[206,]       112.9786 193.86
[207,]       113.4060 208.34
[208,]       112.9786 202.52
[209,]       113.4060 249.34
[210,]       114.2201 245.08
[211,]       112.9786 294.82
[212,]       111.0706 238.92
[213,]       112.9786 176.32
[214,]       113.4060 277.50
[215,]       113.4060 303.38
[216,]       113.4060 232.18
[217,]       112.9786 207.32
[218,]       112.9786 252.96
[219,]       116.2641  57.38
[220,]       110.4828   7.78
[221,]       110.4828  10.96
[222,]       110.4828  22.32
[223,]       110.4828  68.06
[224,]       110.4828   1.50
[225,]       110.4828   0.08
[226,]       110.4828   5.20
[227,]       110.4066   7.14
[228,]       110.4828  -0.30
[229,]       110.4828  -0.40
[230,]       110.4828  11.40
[231,]       110.4828  14.52
[232,]       111.2378 183.14
[233,]       113.4060  46.46
[234,]       110.4828 148.50
[235,]       110.4828 138.80
[236,]       110.4828 224.66
[237,]       114.7810 128.68
[238,]       116.6921 263.22
[239,]       118.7898 228.00
[240,]       112.9786 277.24
[241,]       117.7914 238.78
[242,]       114.4194 305.18
[243,]       118.1769 147.00
[244,]       110.4828  75.58
[245,]       110.4828  11.04
[246,]       110.4828  30.08
[247,]       110.4828  13.06
[248,]       110.4828  10.80
[249,]       110.4828   6.18
[250,]       110.4828   2.60
[251,]       110.4983   0.36
[252,]       111.0211  40.58
[253,]       110.4828  17.22
[254,]       110.4828  -0.50
[255,]       110.4828  91.04
[256,]       109.7286   4.10
[257,]       109.6869   9.38
[258,]       110.4828  25.36
[259,]       110.4828  -2.04
[260,]       110.4828  46.14
[261,]       110.4828  71.48
[262,]       110.4828 105.70
[263,]       110.4828  88.76
[264,]       110.4828  86.30
[265,]       110.4828   8.66
[266,]       110.4828  60.50
[267,]       110.4828  95.74
[268,]       110.4828  -0.14
[269,]       110.4828   9.38
[270,]       111.3433  51.46
[271,]       110.4828  21.24
[272,]       110.4828 165.66
[273,]       110.4828  67.36
[274,]       110.4828  24.64
[275,]       109.7286   0.56
[276,]       110.4828  56.74
[277,]       110.4828 228.62
[278,]       105.5396   3.62
[279,]       110.4828  30.70
[280,]       110.4828  -0.20
[281,]       110.4828   1.10
[282,]       110.9080   0.64
[283,]       110.4828   6.34
[284,]       110.4828   3.32
[285,]       110.4828  68.88
[286,]       110.4828  16.50
[287,]       110.4828  11.36
[288,]       110.4828   1.54
[289,]       109.7286   6.08
[290,]       110.4828   0.58
[291,]       109.7286  15.80
[292,]       110.4828  40.20
[293,]       110.4828 163.94
[294,]       112.9786 172.64
[295,]       110.4828  86.60
[296,]       116.6921  68.88
[297,]       110.4828  -0.52
[298,]       110.4828  23.08
[299,]       110.4828   4.00
[300,]       109.7286  12.28
[301,]       110.4828   1.48
[302,]       109.7286   4.94
[303,]       110.4828  10.36
[304,]       117.0331 277.44
[305,]       113.4168 222.08
[306,]       113.7931 254.50
[307,]       112.9786  32.44
[308,]       118.2726  10.36
[309,]       109.7286  26.08
[310,]       110.2097  14.08
[311,]       110.4828  90.80
[312,]       109.7286   4.14
[313,]       110.4828   0.64
[314,]       110.4828  15.82
[315,]       110.4828  35.16
[316,]       110.4828   8.72
[317,]       110.4828   1.36
[318,]       110.4828  -0.06
[319,]       109.6746  52.34
[320,]       111.8010  -0.10
[321,]       109.7286  10.30
[322,]       111.0211   3.60
[323,]       109.7286   7.40
[324,]       109.7286   7.30
[325,]       110.4983  10.80
[326,]       111.3433   6.30
[327,]       109.7286   1.00
[328,]       111.3433  19.64
[329,]       112.9786 105.16
[330,]       110.4828 238.48
[331,]       113.1779 122.58
[332,]       110.4828 209.90
[333,]       114.2201 237.88
[334,]       112.9786  26.98
[335,]       110.4828  16.70
[336,]       110.4828 184.74
[337,]       111.3560 335.46
[338,]       114.7119 303.66
[339,]       119.5381 266.98
[340,]       118.7898 402.08
[341,]       111.3560 261.26
[342,]       117.9369 308.98
[343,]       119.5381 284.60
[344,]       118.7898  21.68
[345,]       110.4828 268.98
[346,]       105.2860  90.36
[347,]       110.0504 151.42
[348,]       110.4828 142.14
[349,]       110.4828 103.74
[350,]       110.4828  69.92
[351,]       110.4828  14.52
[352,]       110.4828 182.06
[353,]       111.5761 277.28
[354,]       118.7898 266.66
[355,]       120.9336 116.20
[356,]       109.0526 213.44
[357,]       105.2860 103.92
[358,]       109.8052   7.42
[359,]       110.4828   3.52
[360,]       110.4828   0.56
[361,]       110.4828  24.80
[362,]       110.4828  43.02
[363,]       110.4828 150.30
[364,]       110.4828   1.76
[365,]       110.4828  21.44
[366,]       110.4828  24.48
[367,]       110.4828   6.32
[368,]       110.4828  54.44
[369,]       110.4828   0.04
[370,]       110.4828  64.58
[371,]       112.9786  93.64
[372,]       110.4828  20.02
[373,]       110.4828  68.42
[374,]       110.4828  -0.10
[375,]       110.4828  30.32
[376,]       114.4194 256.32
[377,]       114.2201 294.50
[378,]       120.3206 278.32
[379,]       114.2201 202.20
[380,]       114.2201 151.96
[381,]       110.4828 234.18
[382,]       111.5761 352.36
[383,]       108.3754 280.86
[384,]       114.5092 167.24
[385,]       110.4828  85.04
[386,]       110.4828  -0.20
[387,]       110.4828   0.72
[388,]       110.4828  -1.46
[389,]       110.4828   6.46
[390,]       110.4828  11.68
[391,]       110.4828   1.70
[392,]       110.4828  30.32
[393,]       110.4828   0.76
[394,]       110.4828   6.72
[395,]       110.4828  12.16
[396,]       110.4828  19.40
[397,]       110.4828   0.00
[398,]       110.4828  14.52
[399,]       108.1067 102.00
[400,]       105.9670 122.04
[401,]       109.7286 196.74
[402,]       113.4060 132.10
[403,]       109.7286   0.12
[404,]       109.7286  94.16
[405,]       113.7814  10.16
[406,]       109.7286  34.96
[407,]       109.7286   8.56
[408,]       110.4828  -0.48
[409,]       108.1067  18.80
[410,]       110.4828  28.00
[411,]       111.2378  17.98
[412,]       108.1067  -3.24
[413,]       110.4828   1.80
[414,]       109.7286  -1.90
[415,]       110.4828  16.80
[416,]       110.4828   0.38
[417,]       109.7286   0.00
[418,]       110.4828  26.02
[419,]       110.4828   8.78
[420,]       109.7286   0.20

petersenlab::accuracyOverall(
  predicted = y_pred_test_qb,
  actual = data_test_qb_matrix[,"fantasyPoints_lag"],
  dropUndefined = TRUE
)

19.7.7.8 Generate Predictions for Next Season

# Generate model predictions for next season
pred_nextYear_qb <- predict(
  gp_model_fit_qb,
  data = newData_qb_matrix[,pred_vars_qb],
  group_data_pred = newData_qb_matrix[,"gsis_id"],
  group_rand_coef_data_pred = cbind(
    newData_qb_matrix[,"ageCentered20"],
    newData_qb_matrix[,"ageCentered20Quadratic"]),
  predict_var = FALSE,
  pred_latent = FALSE)

newData_qb$fantasyPoints_lag <- pred_nextYear_qb$response_mean

# Merge with player names
newData_qb <- left_join(
  newData_qb,
  nfl_playerIDs %>% select(gsis_id, name),
  by = "gsis_id"
)

Error: object 'nfl_playerIDs' not found

newData_qb %>% 
  arrange(-fantasyPoints_lag) %>% 
  select(name, fantasyPoints_lag, fantasyPoints)

Error in `select()`:
! Can't select columns that don't exist.
✖ Column `name` doesn't exist.

19.8 Conclusion

19.9 Session Info

sessionInfo()

R version 4.5.1 (2025-06-13)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.2 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0

locale:
 [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
 [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
 [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
[10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   

time zone: UTC
tzcode source: system (glibc)

attached base packages:
[1] parallel  stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
 [1] lubridate_1.9.4   forcats_1.0.0     stringr_1.5.1     dplyr_1.1.4      
 [5] purrr_1.0.4       readr_2.1.5       tidyr_1.3.1       tibble_3.3.0     
 [9] tidyverse_2.0.0   gpboost_1.5.8     R6_2.6.1          caret_7.0-1      
[13] lattice_0.22-7    ggplot2_3.5.2     powerjoin_0.1.0   missRanger_2.6.1 
[17] doParallel_1.0.17 iterators_1.0.14  foreach_1.5.2     petersenlab_1.1.5

loaded via a namespace (and not attached):
 [1] DBI_1.2.3            mnormt_2.1.1         pROC_1.18.5         
 [4] gridExtra_2.3        rlang_1.1.6          magrittr_2.0.3      
 [7] compiler_4.5.1       vctrs_0.6.5          reshape2_1.4.4      
[10] quadprog_1.5-8       pkgconfig_2.0.3      fastmap_1.2.0       
[13] backports_1.5.0      pbivnorm_0.6.0       rmarkdown_2.29      
[16] prodlim_2025.04.28   tzdb_0.5.0           xfun_0.52           
[19] jsonlite_2.0.0       recipes_1.3.1        psych_2.5.6         
[22] lavaan_0.6-19        cluster_2.1.8.1      stringi_1.8.7       
[25] RColorBrewer_1.1-3   ranger_0.17.0        parallelly_1.45.0   
[28] rpart_4.1.24         Rcpp_1.0.14          knitr_1.50          
[31] future.apply_1.20.0  base64enc_0.1-3      FNN_1.1.4.1         
[34] Matrix_1.7-3         splines_4.5.1        nnet_7.3-20         
[37] timechange_0.3.0     tidyselect_1.2.1     rstudioapi_0.17.1   
[40] yaml_2.3.10          timeDate_4041.110    codetools_0.2-20    
[43] listenv_0.9.1        plyr_1.8.9           withr_3.0.2         
[46] evaluate_1.0.4       foreign_0.8-90       future_1.58.0       
[49] survival_3.8-3       pillar_1.10.2        checkmate_2.3.2     
[52] stats4_4.5.1         generics_0.1.4       mix_1.0-13          
[55] hms_1.1.3            scales_1.4.0         globals_0.18.0      
[58] xtable_1.8-4         class_7.3-23         glue_1.8.0          
[61] Hmisc_5.2-3          tools_4.5.1          data.table_1.17.6   
[64] ModelMetrics_1.2.2.2 gower_1.0.2          mvtnorm_1.3-3       
[67] grid_4.5.1           mitools_2.4          ipred_0.9-15        
[70] colorspace_2.1-1     nlme_3.1-168         RJSONIO_2.0.0       
[73] htmlTable_2.4.3      Formula_1.2-5        cli_3.6.5           
[76] viridisLite_0.4.2    lava_1.8.1           gtable_0.3.6        
[79] digest_0.6.37        htmlwidgets_1.6.4    farver_2.1.2        
[82] htmltools_0.5.8.1    lifecycle_1.0.4      hardhat_1.4.1       
[85] MASS_7.3-65         

Corporation, M., & Weston, S. (2022). doParallel: Foreach parallel adaptor for the parallel package. https://doi.org/10.32614/CRAN.package.doParallel

Corston, R., & Colman, A. M. (2000). A crash course in SPSS for Windows. Wiley-Blackwell.

Fabri, A. (2022). powerjoin: Extensions of dplyr and fuzzyjoin join functions. https://doi.org/10.32614/CRAN.package.powerjoin

Hu, J., & Szymczak, S. (2023). A review on longitudinal data analysis with random forest. Briefings in Bioinformatics, 24(2). https://doi.org/10.1093/bib/bbad002

Kuhn, M. (2024). caret: Classification and regression training. https://doi.org/10.32614/CRAN.package.caret

Mayer, M. (2024). missRanger: Fast imputation of missing values. https://doi.org/10.32614/CRAN.package.missRanger